Well, if you use educated speculation (which I'm doing right now

) those Hammond amps were most likely DESIGNED during the same era as the 7591's.
So, you can eliminate the really old designs. . . AV, BV, CV, BV, M, M1, M2. You can also rule out the H-40, HR-40, P-40, PR-40, and Q-40, QR-40 tone cabinets. 6V6's or 6BQ5's in those.
So, that means no B3, C3, or A-100 because they all used the same internals in different cabinets; and the amp was an earlier design (H-AO-28) which used 6V6's. Some later model A series used the H-AO-39 which used 6BQ5's. The Porta B also used 6BQ5's in their H-AO-47 amp.
The M3, M101, and M102 used an H-AO-29 amp which also used 6V6's
Early versions of the M100 aslo used an H-AO-35 reverb amp that used 6BQ5's, and the H-AO-44 reverb amp in the later models. But, still no 7591's.
The H-100 series used an H-AO-70 as the main amp which also used 6BQ5's. . . as did the L series in their H-AO-43 amp.
However, the E series designed in 1964 and produced in June of 1965 used 2-7591's in their H-AO-63 amp.
The K series also used 2-7591's in their H-AO-65 amp.
I don't have data for the H-AO-68 amp (or which Hammond model used it), but I'm fairly sure that one also used 2-7591's.
Hope this reply helped.
. . Falcon